package 高频题;

public class 最小路径和_64 {
    public int minPathSum(int[][] grid) {
        if (grid.length == 0) {
            return 0;
        }

        //dp[i][j]：到下标(i,j)的最小和
        int[][] dp = new int[grid.length][grid[0].length];


        //base case
        dp[0][0] = grid[0][0];
        for (int i = 1; i < grid.length; i++) {
            //第一列
            dp[i][0] = grid[i][0] + dp[i - 1][0];
        }
        for (int i = 1; i < grid[0].length; i++) {
            //第一行
            dp[0][i] = grid[0][i] + dp[0][i - 1];
        }

        //状态转移
        for (int i = 1; i < grid.length; i++) {
            for (int j = 1; j < grid[0].length; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[grid.length - 1][grid[0].length - 1];
    }
}
